Parameter Synthesis for Probabilistic Hyperproperties

In this paper, we study the parameter synthesis problem for probabilistic hyperproperties. A probabilistic hyperproperty stipulates quantitative dependencies among a set of executions. In particular, we solve the following problem: given a probabilistic hyperproperty ψ and discrete-time Markov chain D with parametric transition probabilities, compute regions of parameter configurations that instantiate D to satisfy ψ, and regions that lead to violation. We address this problem for a fragment of the temporal logic HyperPCTL that allows expressing quantitative reachability relation among a set of computation trees. We illustrate the application of our technique in the areas of differential privacy, probabilistic nonintereference, and probabilistic conformance.